module module high

`IndisputableMonolith.Theology.SubstrateIndependentMonotheism`

This module defines the Substrate type and associated predicates for substrate-independent monotheism in Recognition Science. A substrate carries a natural-number phase (0 canonical), integer σ-charge, and label; the module then classifies divine, monotheistic, polytheistic, and atheistic cases via trichotomy and total-σ results. A working physicist or philosopher of foundations would cite these definitions when examining monotheism as the canonical outcome. The module is purely definitional with no proofs.

claimA substrate is a triple $(p, c, l)$ where $p \in \mathbb{N}$ (phase, $p=0$ canonical), $c \in \mathbb{Z}$ ($\\-charge), and $l$ a label. The module defines predicates isDivine, isMonotheistic, isPolytheistic, isAtheistic together with a trichotomy on total $\sigma$ and the statements that polytheism with two occupants violates canonicity while monotheism realizes the canonical $\sigma$.

background

The module sits in the Theology domain and imports Constants (defining the RS time quantum $\tau_0 = 1$ tick) and Cost. Its central object is the Substrate structure whose doc-comment states: a substrate has a phase $\in \mathbb{N}$ (0 = canonical), a $\sigma$-charge $\in \mathbb{Z}$, and a label. From this base the module introduces the predicates isDivine, Theology, divine, isMonotheistic, isPolytheistic, isAtheistic, trichotomy, totalSigma, polytheistic_two_violates_canonical, monotheistic_canonical_sigma, and unique_occupant_is_monotheistic.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the Substrate definition and the monotheistic_canonical_sigma and unique_occupant_is_monotheistic results that anchor the theology section. It thereby supplies the formal substrate for any later argument that monotheism is the canonical configuration under the Recognition Composition Law and the eight-tick octave.

scope and limits

Does not assert existence of any divine entity.
Does not derive numerical predictions or link to the phi-ladder.
Does not reference J-cost, defectDist, or the forcing chain T0-T8.
Does not connect $\sigma$-charge to mass formulas or the alpha band.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (16)

structure Substrate L46
def isDivine L55
abbrev Theology L67
def divine L72
def isMonotheistic L77
def isPolytheistic L82
def isAtheistic L86
theorem trichotomy L91
def totalSigma L106
theorem polytheistic_two_violates_canonical L110
theorem monotheistic_canonical_sigma L118
theorem unique_occupant_is_monotheistic L125
theorem one_god_with_creatures_is_monotheistic L133
structure SubstrateIndependentMonotheismCert L141
def substrateIndependentMonotheismCert L154
theorem substrate_monotheism_one_statement L165